The Discrete Fourier Transform spread Orthogonal Frequency Division Multiplexing (DFT-spread OFDM) modulation is more and more used in the telecommunication technologies.
For example, DFT-spread OFDM is used to implement the uplink transmissions in 3GPP/LTE networks under the acronym of SC-FDMA (Single Carrier Frequency Division Multiple Access) as disclosed in Non Patent Literature 1.
For example, DFT-spread OFDM is used to implement the satellite component of the DVB-NGH system hybrid profile (see Non Patent Literature 2).
In the two aforementioned systems, DFT-spread OFDM was selected due to its low power envelope fluctuations, a key enabler for reducing the power consumption at the transmitter. DFT-spread OFDM actually combines the suitable properties of Single Carrier (SC) and Multiple Carrier (MC) waveforms, i.e. the low power fluctuations of Single Carrier modulations with the flexibility and low receiver complexity of Multiple Carrier modulations.
In the DFT-spread OFDM modulation, the constellation samples are first spread in frequency by means of a DFT. After addition of null sub-carriers at the two band edges, the spread symbols are OFDM modulated to obtain a signal with the expected spectral shape. The combination of a DFT for spreading and an IDFT for modulation, provides a resulting signal that may be simply understood as the oversampled version of the original samples that would be filtered out with a Dirichlet waveform, also known as Dirichlet kernel, the equivalent in DFT interpolation of the cardinal sine function or sine function in continuous time interpolation.
This is actually the principle of the well-known FFT or Fourier oversampling algorithm. It may be considered that the DFT-spread OFDM modulation can be interpreted as an alternative to basic time domain filtering to implement the generation of a Single Carrier signal. Due to the circularity of the DFT convolution, the first and last samples over each OFDM symbols are significantly correlated to each other over a number of more or less 4-6×N′/K′ samples, i.e. the first 2 or 3 lobes of the Dirichlet waveform, where N′ is the number of samples after OFDM modulation and K′ is the number of samples after the DFT transform.
The classical OFDM modulation is particularly well suited for frequency selective channels as the impact of the channel can readily be retrieved by means of a simple one-tap equalizer over each sub-carrier. To compute the equalizer coefficients, the receiver needs to estimate the channel coefficients over all the data sub-carriers.
An accurate channel estimation appears as a key functionality of the OFDM receiver. The channel is generally estimated using reference symbols also called pilots known at the receiver. Unlike with Single Carrier signals, it is possible in OFDM to adjust the ratio data/pilot according to the channel properties in both the frequency and time domains. For instance, if the channel coherence bandwidth is very high but the channel changes rapidly, it is possible to insert only a few pilots in the frequency domain, for example 1 pilot every γ>>1 sub-carriers, regularly spaced in time, for example one OFDM symbol every few δ symbols. It is even possible to change the position of the pilots from time to time.
This is one of the main advantages of the OFDM modulation with respect to Single Carrier modulation and DFT-spread OFDM modulation.
If the DFT-spread OFDM modulation benefits from its OFDM lineage for the equalization, it is not the case for the insertion of pilots. Indeed, the low power fluctuations of DFT-spread OFDM signal envelope result from the OFDM modulation of DFT-spread symbols. Any arbitrary alteration of the spread sub-carriers through for instance the insertion of reference sub-carriers may break the Peak to Average Power Ratio (PAPR) properties of the signal. For that reason, the 3GPP/LTE uplink system specifies a full pilot, i.e. all the modulated sub-carriers of a symbol carrying pilots, directly inserted in the frequency domain as a Zadoff-Chu sequence. Zadoff-Chu sequences have constant amplitude and remain a Zadoff-Chu sequence after a DFT. The transmitted pilot thus keeps the good PAPR properties of a Single Carrier signal.
In order to reduce the pilot overhead, the DVB-NGH system specifies a pilot that combines data and reference information (hereafter called hybrid pilot symbol). Data are obtained by applying a spreading DFT over a block of data with a length equal to half the size of a DFT used if no pilot is inserted. Then, spread data are interleaved one every two sub-carriers along with a spread Zadoff-Chu sequence (also with half length with respect to a regular data symbol). For each component of the reference symbol (data and pilots), the resulting signal is simply the oversampled version of two consecutive copies of the original half-length sequence.
As the sum of two Single Carrier signals, the resulting signal is no more a pure SC signal.